The assumption would be that Ventura or any manager would have the power not to start Dunn in the field or as the DH and using him as a pinch hitter. I don't know if that amounts to benching him. With Beckham out and Viciedo out, that might be impractical.

If Beckham were in the lineup at second, you could use the DH to get both Gillaspie and Keppinger in the lineup. You could use the DH to give Konerko the day off without being stuck with Dunn's defense at first. You could have Viciedo in the lineup without having to worry about his defense in left. Really, I think the White Sox would have a better offense without a fulltime DH. All of those options would provide a better offensive lineup. At the start of the season there were better options than Dunn for the DH role, but there was also the hope that he wasn't going to be the black hole on offense that he was last season and the season before that.

I'm not sure what consequences there would be if Dunn were to become a full-time pinch-hitter instead of a full-time DH, where he hurts the team the least as a starter. Not starting Dunn wouldn't hurt the Sox offensively. Fans seem fed up with seeing him in the lineup, so it couldn't alienate the fanbase. You would be playing one roster spot short, but on the upside, you wouldn't have Dunn in the lineup. I can't imagine it would decrease Dunn's trade value because I can't imagine that such would be possible.

And I'm not sure it would be such as bad thing if Dunn demanded a trade. Unless the rules have changed, if Dunn demanded a trade, and the Sox couldn't accomodate him, he would have the option of abadnoning his contract and becoming a free agent. I can't imagine he would have grounds for grievance if he where benched. If you're hitting less than .220, which has been Dunn's history with the Sox except for a couple of months in 2012, you really can't complain about being benched.